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```896                              Appendix II.

the main-valve circle, and c K that shewing relative motion of the

two valves.    Join H D, and produce to w, making GW II FD, and

join K j.    We must prove j c = F D, the difference- or relative-                   ;

motion.    Now F, D, j, and w are right angles (Euc. III. 31), and

G H = K c; therefore JC=GW = FD. Hence the radii-vector of the

vertical shading shews diminishing opening of expansion plate,

which becomes zero when c s = the R circle radius or circle of

negative  steam lap  of expansion plates.    Also  the  horizontal        *           ;

bine the two areas by drawing radial lines through c, taking the

shorter intercept of the two, and placing radially on base p Y, and

thus obtain the curve PXY, shewing that opening from p to x is

governed by main valve, and closing from x to Y by expansion                   I

plate: the two spaces being equal at x u.                                                       \

P. 686. Condensers. — Wherever the supply  of cooling

j I   j                       water is limited, the Evaporative  Condenser^ Fig. 858,  may be

adopted. The exhaust steam A passes through a large number of
pipes F, cooled externally, and the condensed steam is returned to
hot well by pump B. The upper trough c is kept filled with
water, which trickles over the pipes into the lower trough D, and
is then returned by circulating pump G to c, the evaporation
;                       loss being made good from the main at E. Whereas in the usual

j                       condensers the steam heat is simply used to raise the temperature

!                       of water, requiring about 20 Ibs. water per Ib. of steam (see p. 598),

this condenser evaporates a large portion of the cooling water, thus
causing each Ib. of evaporated water to abstract the heat in i Ib.
of steam or thereabouts; hence the weight of cooling water may
be merely equal to that of the condensed steam. In practice it is
often less, for radiation and conduction do some of the work
The evaporation is increased some 50% if fan draught is used;
and 10 sq. ft. of pipe surface per L H.P. is adopted, as against
i or 2 with surface condensers. The joints must be Specially
good, but a 24 in. or 26 in. vacuum may be obtained, and still
better results if the steam and water currents be opposed in
direction. External incrustation must be removed at times.

Various cooling systems are also adopted to economise con-
densation water. In Fig. 859, A is an ' independent' Worthing-
ton jet condenser, where B is the steam cylinder and c the air```